Using spring repulsions to model entanglement interactions in Brownian dynamics simulations of bead–spring chains

Abstract

We develop a bead–spring Brownian dynamics model for simulating the topological interactions between polymers and thin obstacles and apply this method to electrophoretically translating DNA strands interacting with an immovable post. The use of a bead–spring method allows for the simulation of entanglement interactions of polymer chains too long to be simulated using bead–rod or pearl necklace models. Using stiff “FENE-Fraenkel” springs, we are able to model short chains as well. Our new method determines the shortest distance between a spring and the post, calculates a repulsive force inversely related to this distance using an exponential potential, and corrects for the rare situation when a spring passes beyond the post despite the repulsive interaction. As an example problem, we consider single-chain collisions with a single post in weak electric fields. We explore a wide range of chain lengths (25–1,515 Kuhn steps), and we find that the average delay produced by the collision is a function of both the chain length and the Peclet number. Chains of all lengths reach the same upper limit at high Peclet number, but they follow separate curves with similar slopes at lower Peclet number. Our results are consistent with published results for a 25-Kuhn-step chain at Peclet number Pe = 10. Our new method is a general one that allows us to compute the effects of entanglements in systems with rare entanglements and long chains that cannot be simulated by other more microscopic methods.